RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 12. Circles

Subject: Maths - Class 10th

Q. No. 48 of Multiple Choice Questions (MCQ)

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48

In the given figure, AP, AQ and BC are tangents to the circle. If AB = 5 cm, AC = 6 cm and BC = 4 cm then the length of AP is

Let tangent BC touch the circle at point R


As we know tangents drawn from an external point to a circle are equal.


We have


AP = AQ


[tangents from point A]


BP = BR …[1]


[tangents from point B]


CQ = CR …[2]


[tangents from point C]


Now,


AP = AQ


AB + BP = AC + CQ


5 + BR = 6 + CR [From 1 and 2]


CR = BR - 1 …[3]


Now,


BC = 4 cm


BR + CR = 4


BR + BR - 1 = 4 [Using 3]


2BR = 5 cm


BR = 2.5 cm


BP = BR = 2.5 cm [Using 2]


AP = AB + BP = 5 + 2.5 = 7.5 cm

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